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I am analyzing a path analysis model with one endogenous variable (the primary outcome) being categorical (binary) and the other (a potential mediator) being continuous. Is the aim in my path analysis the same as it is when all outcomes are continuous, to reproduce as closely as possible the variancecovariance matrix? 

bmuthen posted on Thursday, January 08, 2004  10:09 am



In this case you are using a limitedinformation weighted leastsquares where the model is fitted to sampleestimated multivariate probit thresholds, slopes, and residual correlations. Same number of quantities are used for the fitting but different ones from the continuous case of means, variances, and covariances. 


Thank you. I am planning to submit my paper for publication. What would you recommend presenting in the results section, a correlation matrix does not seem appropriate given the categorical outcome. Or are the fit indices plus a figure with standardized path coefficients sufficient? 

bmuthen posted on Thursday, January 08, 2004  10:17 am



I think what you suggest is good, but also add unstandardized coefficients and their SEs. 

Anonymous posted on Monday, December 13, 2004  7:26 am



I am experimenting with the examples in the Mplus guide (ex 3.12)that use binary outcomes as dependent/endogenous measures. I was wondering if there are any peer reviewed publications that have used this technique? I would like to use this in a paper that I am planning to send out for publication and I would like to cite some studies that do this. Thank you. 

bmuthen posted on Monday, December 13, 2004  8:28 am



You many want to look at the article by Xie on the Mplus web site, Reference section. 

Anonymous posted on Saturday, May 21, 2005  2:32 pm



Hi, there is an article regarding SEM of discrete data by Winship and Mare (1983) in the American Journal of Sociology ("Structural Equations and Path Analysis for Discrete Data."). If you are aware of it, could you please let me know the similaries/differences between their estimate and the MPlus estimation of discrete variables? Thanks! Tom 

bmuthen posted on Saturday, May 21, 2005  4:19 pm



Yes, I am aware of this article, but I don't recall the content other than that I think a different tack was taken than in my work from the late 70's and early 80's. I should take another look at the article  do you have a pdf handy so I can refresh my memory of it? 

bmuthen posted on Sunday, May 22, 2005  2:47 pm



Thanks for sending the WinshipMare (1983) article. Its relationship to the categorical variable modeling in Mplus is clear from examples like the one they start off with  social background (x, say) influencing the mediator of getting a college degree (y, say), influencing unemployment (z, say). As in the econometric literature, they make it clear that while x>y is naturally a logit or probit regression, the specification of the influence of the mediator on z may either use the 0/1 dummy variable y itself or an underlying continuous latent response variable y* (that gives rise to y=1 instead of y=0 when exceeding a threshold). They discuss ML estimation using probit for some simple special cases. The literature indicates that ML using y* gives a different loglikelihood than ML using y, and as pointed out in the article different applications naturally call for different choices. Using the simple example above, Mplus makes the y* choice when using probit modeling and (limitedinformation) WLS type estimators that I developed in my 19781984 work on LISCOMP. More recently, the y choice has also been added to Mplus using logit with ML. We have plans to add the other combinations of using y/y*, probit/logit, and ML/WLS. When all observed dependent variables are categorical, Mplus also offers the Feinberginspired "causal" modeling mentioned in the article. This is with multiple latent class variables as mentioned in Chapter 13 of the Version 3 User's Guide, where a latent class variable can be specified to be perfectly measured by an observed categorical variable (this feature also enables loglinear modeling of frequency table data, using the alternative loglinear parameterization). Hope this answers your question. 

Anonymous posted on Wednesday, June 08, 2005  2:36 pm



I have two endogenous variables, Y1 is binary (0/1), and the other (Y2) has three categories, which are coded as 0/1/2: ... CATEGORICAL IS Y1; NOMINAL IS Y2; Y1 ON Y2 X1 X2 Y2#1 Y2#2 ON X1 X3 In the second equation (Y2 is the dependent variable), I use Y2=0 as the comparison baseline, but how can I make Y2=0 as the comparison baseline in the first equation when Y2 is an independent variable? 


A nominal variable cannot be a mediating variable in Mplus. It is unclear how to deal this situation because it would be treated as nominal when it is a dependent variable but would need to be treated as a set of dummy variables as an independent variable. 

Anonymous posted on Wednesday, June 08, 2005  6:43 pm



Thanks a lot. If there is an order between the three categories of Y2 (0>1>2), can I treat Y2 as ordered categorical (ordianal)? In another word, can an ordinal variable (ordered categorical) be a mediating variable in MPLUS? Again, I want one of the three categories (e.g., "Y2=0") as the comparison baseline in both equations (i.e., in the equation when Y2 is the dependent variable and in the equation when Y2 is an independent variable). Thanks again! 


Yes, ordinal variables can be used as mediating variables. With weighted least squares estimation, probit regression is obtained. With maximum likelihood estimation, logistic regression is obtained. There is no reference category with ordinal dependent variables. 

Anonymous posted on Thursday, June 09, 2005  9:28 am



Thanks a lot. If there is no reference category with ordinal dependent variables, how I can interpret the results (for both cases: when the ordinal variable is an independent variable and when it is a dependent variable)? If an ordinal variable only has three categories, it may not be appropriate to see it as continuous. 

Anonymous posted on Thursday, June 09, 2005  4:19 pm



Please allow me to rephrase the above question. I now know how to interpret ordinal logit regression. And my three questions are: (1) In the example above, if Y2 is ordinal, it is fine for it to be a dependent variable in the second equation (Y2 ON X1 X3), but how to treat it when it is an independent variable in the first equation (Y1 ON Y2 X1 X2)? Y2 has only three categories (0/1/2) so that I doubt we can treat it as a continuous independent variable, and I wonder if it is appropriate to generate two dummy variables corresponding to Y2=1 and Y2=2 to replace Y2 in the first equation (Y1 ON Y2 X1 X2). Alternatively, can I do this in the following way? First, generate three dummy variables Y20, Y21, and Y22, corresponding to Y2=0, Y2=1, and Y2=2. Then, run equations: … CATEGORICAL IS Y1 Y21 Y22; Y1 ON Y21 Y22 X1 X2 Y21 Y22 ON X1 X3 The following questions are: (2) Should I specify Y20 as CATEGORICAL as well? (3) Should I add Y20 as a dependent variable in the second equation? If I add Y20 (or don’t add it), is there any technical problem? 

bmuthen posted on Thursday, June 09, 2005  6:28 pm



(1) The default option in Mplus is to use WLSMV which takes a probit approach in which case the equation where Y2 is an independent variable, an underlying continuous latent response variable Y2* is used to predict Y1. For a discussion of related matters see the Xie article on the Mplus web site and also the WinshipMare 1983 article discussed earlier in this forum. Don't create dummy Y2 variables if you want to treat it as ordinal. Stay with the approach I just mentioned. (2)(3) Not relevant given my answers above. 

Anonymous posted on Thursday, June 09, 2005  8:20 pm



Thanks a lot! Two more questions regarding interpretation: (1) When the ordered categorical (ordinal) variable is an independent variable, since it is treated as a latent continuous variable, can I interpret its coefficient like interpreting a continuous variable? (2) When the ordered categorical (ordinal) variable is a dependent variable, how to interpret the coefficients of independent variables in a meaningful way? (now the dependent variable is not a binary variable but has more than two categories) 

bmuthen posted on Friday, June 10, 2005  6:16 am



(1) Yes (2) The slope can be interpreted the same as with a continuous dependent variable given that an ordinal dependent variable can be seen as a continuous latent response variable that exceeds thresholds to give the various outcome categories. There is therefore only one slope. See also Appendix 1 in the Technical Appendices on the Mplus web site. 


Hi, I have several questions concerning a SEM analysis I am trying to run. I have some categorical variables and some other variables with extreme missing values. I do not have any latent variables in my model. The analysis always terminates normally but I don’t know if I can trust the results, although they are very stable. Analysis: Type= missing; Estimator= mlr; Integration= montecarlo; Coverage=.04; Mcseed=331; (mcseed I tried because the error said something about a starting value.. but it makes no difference) In the output I see 2 warnings / errors: A) THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.380D15. PROBLEM INVOLVING PARAMETER 354. B) ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL. THE FOLLOWING PARAMETERS WERE FIXED: 190 603 119 134 611 Error B only appeared when I included 17 dummies in my model (for the 18 schoolsthis was originally a categorical variable) After these errors the output states that the model estimation terminated normally. 1.What do these errors mean? 2.How can I correct for them? 3.Can I get fit indices like TLI CFI by putting H1 in the type command? Thanks, Liesbeth PS: I will attend to your course in Utrecht although it is not specifically what I am doing… can I bring my output also to the course? 


This error message is serious. Your model has a lot of parameters. I wonder how large your sample is. You need more observations than parameters. I can't say much more without more information. Please send your input, data, output, and license number to support@statmodel.com. I don't think H1 is available with the estimator you are using but I would need to see your entire model to answer that. It is unlikely that we will have time to look at output at the Utrecht meeting. You should send your questions to support. 

Wendong Li posted on Sunday, February 21, 2010  3:51 am



Hi, I am running a model with all continuous variables but one categorical variable as a control. I am not interested in whether there is any difference among different categories of this variable and just want to partial out its impact. Can I just put it in the model, tell the program it is categorical and then regress the outcome variable on it? Thanks in advance! 


You can include it and regress the outcome variable on it but you should not put it on the CATEGORICAL list. This list is for dependent variables only. The model is estimated conditioned on the observed exogenous variables and their scale is not relevant. 

Wendong Li posted on Sunday, February 21, 2010  10:40 pm



Thanks a lot for your input, Linda! 

haxha posted on Monday, November 08, 2010  10:18 pm



Hi Linda, in page 496 of the manual version 5, you indicate that Bootstrap is not available for MLR due to the parameter estimates and bootstrap standard errors for these estimators not differing from those of ML. I am not quiet sure I understand this? Would this mean that that there is no need to use bootstrap with MLR because the results are identical? Sorry I'm a novice in Path Analysis and would like to use some type of simulation to ensure that my results are not biased. Any suggestions other than crossvalidation and holdover sampling method? 


Yes, the parameter estimates are the same for ML, MLR, and MLF. So if you used bootstrapping with any one of these to obtain bootstrapped standard errors, the results would be identical. For simplicity we make bootstrap available only with ML. 

Regan posted on Saturday, November 20, 2010  12:07 am



Professors Two questions: 1) After reading a response on the site, I wanted to clarify that if a binary 0/1 bvariable is included as a mediator, it does not have to be declared as categorical in the "CATEGORICAL ARE" command, ( I ask because I know this must be done for dependent outcome variables, however, in an SEM class, it was said that all variables with arrows going into them were considered dependent) 2)Are pvalues available for correlations obtained in Mplus? I see that users publish correlations with pvalues, but these do not seem to be part of the Mplus output. Thanks 


1. A mediator is a dependent variable and if it is binary it should be placed on the CATEGORICAL list. 2. Not for sample correlations. You can estimate a model of correlations or covariances and obtain pvalues in this way. 


Hi, This is a very basic question so apologies in advance. I have a mediation model comprising 5 continuous latent constructs (1xIV; 1xM; 3xDV)and three control measures (the latter are directly observed). One of my control measures is binary (0=no/1=yes). Would I be correct in thinking that I don't enter the binary measure on the line 'CATEGORICAL ARE' as it's not the DV? When I don't specify this measure as categorical the model runs fine. However, when I do specify it as categorical I recieve a meassage that I must use montecarlo integration and that I cannot estimate indirect effects. Using this integration technique runs the data, but I don't get any fit indices for the model. Thanks, Stacey 


Only dependent variables should be placed on the CATEGORICAL list. Observed exogenous variables should not be put on this list. 


Hi, If i have a binary outcome variable(1=adopt, and 0=nonadopt)and i want to measure the impact of factors affecting the adoption, these factors are continuous latent variables but are divided to four main factors; f1, f2, f3, and f4. the question is: do i have to run Path analysis with categorical dependent variable as in example 3.12? If yes, i have used ML to get logistic regression results, but the second question is, do these results target the adopt category or nonadopt? in other words, if i want to say that f1 affects positively u1? in this case is u1 adopt or non adopt category? I hope you get my meaning. Thanks, 


Example 3.12 uses weighted least squares not maximum likelihood. This yields probit regression coefficients. For maximum likelihood and logistic regression, you must add ESTIMATOR= ML; to the ANALYSIS command. Note that if your factor have categorical factor indicators, this would result in four dimensions of integration. U1 is adopt. It is the highest category. 


Hello, I am testing the extent to which delinquent peers and depression condition the relationship between victimization and offending (offending is a binary outcome (1=offending 0=no offending). I conducted analysis on the overall sample as well as on each gender group. The results are very similar, with an exception of a few parameter estimates. My question is: how appropriate is to conduct coefficient comparison test across gender groups without running a multiple group analysis? If yes, which formula can I use? Thank you. 


You get a statistical test of gender equality if you do a multiplegroup analysis. I think that is highly desirable. 


Hello, I am using mplus 5 to run an ordinal regression and path analysis model. i have missing values, but less than 10%. The program excludes all observations that have missing values from the analysis. could you please tell me how can i insert all observations i have in my analysis. Thanks Owis 


Version 5 has TYPE=MISSING as the default. Cases must be excluded that have missing on observed exogenous x variables. This is because missing data theory does not apply to these variables. If you mention their means, variances, or covariances in the MODEL command, they will be treated as dependent variables and distributional assumptions will be made about them. The subjects will not, however, be excluded from the analysis. 


Thanks for your response, but how can i mention their means. do you mean put then in brackets? 


This is my command. could you please tell me how to mention the mean or the variance in the MODEL command. Thanks Owis TITLE: this is an example of a logistic regression for a categorical observed dependent variable with two covariates DATA: FILE IS C:\Users\Admin\Desktop\MGH\path3.dat; VARIABLE: NAMES ARE smo em sym pf ef sf re bmi age fev gender act5 actc; USEVARIABLES ARE smo em sym pf ef sf re bmi age fev gender act5; CATEGORICAL IS act5; missing = .; ANALYSIS: ESTIMATOR = ML; MODEL: act5 ON smo em sym pf ef sf re bmi age fev gender; 


MODEL: act5 ON smo em sym pf ef sf re bmi age fev gender; smo em sym pf ef sf re bmi age fev gender; 


Thanks a lot. Usually i use SAS for statistical analysis. in SAS we can define the categorical variable (i.e reference group). Does Mplus do that? Thanks Owis 


You can use the DEFINE command to create a set of dummy variables for a categorical covariate. 


Actually i have the categories already. but in the results interpretation, we should have reference group in categorical variables. for example, male are more likely to have the disease. so the reference group is male and the interpretation is for male not female. Thanks Owis 


With a dummy variable, 0 is the reference group and 1 is the group for which the effect is relevant. 


Thanks a lot Linda 


Hi Linda again, i did as what you told me last time regarding analyse all available values. you told me to mention their means, variances, or covariances in the MODEL command. you gave me the command, but it is the covariances and the is no covariances between these exogenous variables. could you please tell me how can i mention just their means or variances. Thanks Owis 


I gave you the command for the variances not the covariances. If you have further problems with this, please send your output and license number to support@statmodel.com. 

chris pp posted on Thursday, April 05, 2012  9:59 pm



Hi! I'm running a SEM where one of the variables ('nage') is categorical (dichotomous) and is modelled as a predictor of one continous variable, and an outcome of another continuous variable. There seems to be less output on the standardized results when this variable is set as categorical (only showing StdYA under the STANDARDIZED MODEL RESULTS). Are there additional commands required to generate more output in this case? The syntax is: USEVARIABLES ARE edu cfit nage social selfr pa pop; MISSING ARE ALL(999); CATEGORICAL IS nage; MODEL: sr BY selfr@0.78; selfr@.15; soc BY social@.72; social@.17; sr ON edu cfit; soc ON sr pop cfit; pa ON pop soc; nage ON edu; cfit ON edu; pop ON nage edu; 


With the default WLSMV estimator, standard errors for the standardized solution are not available when the model has covariates. 

Aylin posted on Monday, June 25, 2012  8:39 am



Dear Professors, I am running the following model: (using WLSMV estimator) Usevariables are vic IQ daw emot PL12 PL18 dep sex; Categorical are vic daw PL12 PL18 dep; Analysis: Parameterization = theta; Model: IQ with daw; vic with emot; vic on IQ daw; emot on IQ daw; dept with PL12 ; vic emot daw IQ on sex; dept PL12 on sex vic emot IQ daw; PL18 on sex dept PL12 vic emot IQ daw; So my questions are: 1) As I am using both categorical and continuous variables does that mean my path analysis consists of both linear and probit regressions? So "emo (continuous) on daw (categorical) = linear regression" and "vic (categorical) on IQ (continuous) = probit regqression" is this correct? 2) Then what are the correlations? for example "IQ (continuous) with daw (categorical)" is this a coveriance or a tetrachoric correlation? Thank you very much. 


1. If the dependent variable is continuous, the regression coefficient is linear. If the dependent variable is categorical, the regression coefficient is probit. 2. Continuous with categorical is a biserial or polyserial correlation. Binary with binary is a tetrachoric correlation. 

Aylin posted on Monday, June 25, 2012  10:28 am



Thank you very much 

Ellen posted on Thursday, April 10, 2014  8:08 am



Hi I am doing a path analysis that includes a dicotomous endogenous variable(Y1) and censored endogenous variables(Y2, Y3). I want to test the relationship Y2 with Y3(non recursive model) X1, X2 > Y1(dicotomous) Y1 > Y2(censored) Y1 > Y3(censored) Y2 > Y3 Y3 > Y2 But I get an error message that the latent variable covariance matrix(psi) is not positive definite.PROBLEM INVOLVING VARIABLE Y3. I checked TECH 4, but I don't know what is wrong. Could you help? 


Please send the output and your license number to support@statmodel.com. 

Marie Alice posted on Thursday, March 19, 2015  12:28 am



I am doing path analysis with a continuous outcome variable. My understanding is that when an independent variable is categorical, it is not an issue. 1. But when I have a mediator (parental aspiration: university and above=1) that is categorical, should I specify so using the command "categorical="? 2. When I have an independent variable, that is controlled by another variable, should I also specify it as categorical? (For example, in modelling single parent>income>child's achievement, I also model parent's education>single parent to control for selection bias. In such case, should I specify single parent as categorical?) I ask, as I see that the coefficients change dramatically whether I specify the variable as categorical or not. 


You should specify the scale of any endogenous dependent variable that you want to treat other than as continuous. The scale of observed exogenous variables should not be specified. 

Marie Alice posted on Thursday, March 19, 2015  6:39 pm



Thank you for response. So for that path (pointing into a dichotomous variable), I should interpret the coefficient as a logit coefficient, whereas all other variables (pointing into continuous variables) are regression coefficients? 


With WLSMV, you obtain a probit regression coefficient for a categorical dependent variable. With ML, you obtain a logistic regression coefficient for a categorical dependent variable as the default. You can request a probit regression coefficient using the LINK option. Linear regression coefficients are obtained for continuous dependent variables. 


Hi Dr. Muthen I want to ask you about path analysis with ordered categorical variables. I have 6 independent variables (ordered categorical) treated as exogenous variables and 2 dependent variables (endogenous var.) one of them is mediator. My question now how can i analysis this type of path analysis when the dependent variables are latent variables and the independent vars. are ordered categorical and can i use probit regression on indep. vars. and put a zero variables in latent vars. many thanks in advance 


Don't put IVs on your categorical list; that should be done only to DVs. Apart from that, your setting is standard SEM. 


Many thanks to you for your response i want to ask you what about latent variables now are a dependent variables so can i put a zero values for that? Regarda 


With latent variables as dependent variables you use regular linear regression even though the DV is latent. I don't know what you mean by putting a zero value for that. 


because and as you know the latent variables are unobserved so there is no values for these variables. can i put a zero's matrix for these variables. Regards 


What is your aim  what is it that you are trying to do? 


Thank you for your response I want to estimate the parameters of path analysis using Bayesian inference but i cannot leave the latent variables without any values. Can i use zero's matrix for that? Regards 


I still don't understand what you are doing. If you want to estimate a model with latent variables you don't need to give the latent variables values. 

sh wong posted on Thursday, May 14, 2015  9:03 am



Hi, I'm trying to run path analysis with one dichotomous dependent variable and few continuous dependent variables similar to example 3.14. 1. May I know which part of output should I refer to for the path coefficients? 2. What kind of Rsquare is it and how can I interpret it? 3. Can I have a equation similar to running a multiple linear regression of continuous variables, such as u1 = coeff1(y1) + coeff2(y2) + coeff3 (x1) + coeff4 (x2) + coeff5 (x3) ? Thank you very much. 


You can learn about these matters in our Topic 2 short course video and handout on our website. Short answers (but these Q & A's is not the way to learn about this topic). 1. The ON statements. 2. Rsquare for the continuous latent response variable u1* for the DV u1. 3. Yes for u1*. 

sh wong posted on Friday, May 15, 2015  8:44 am



Thanks very much Dr. Muthen. May I ask further for I'm a beginner in statistical modelling. 1. Should I base on the StdYX Estimate column under standardized model results section for the path coefficients ? 2. Base on the standardized model results, I can generate the equation with the StdYX Estimate: u1* = coeff1(y1) + coeff2(y2) + coeff4 (x2). But how can I find the corresponding coefficients when all the variables are included, i.e. u1* = coeff1(y1) + coeff2(y2) + coeff3 (x1) + coeff4 (x2) + coeff5 (x3) Which output setting should I make to generate the results? Please also correct me if my understanding on the above is wrong. Thank you very much. 


1. Not for predicting u1*. 2. Mplus does not provide individual estimated u* values. Typically one doesn't look at them. You may want to ask these types of questions on SEMNET. 

sh wong posted on Friday, May 15, 2015  7:47 pm



Thank you. I would post the questions on SEMNET then. Thanks. 


And you really want to study our Topic 2 course on our website because it gives many of the answers. 

sh wong posted on Sunday, May 17, 2015  9:39 am



Thanks Dr. Muthen. I've studied the topic 2 course and that helps cleared some of my questions. In Mplus, I understand that WLSMV is the default estimator. However, when I try using ML estimation which uses logit regression, no model fit indices of Chi2, RMSEA, CFI, SRMR, etc could be found. Since I want to do a path analysis and to test the model fit, is it a must to use WLSMV? If so, how should I interpret WRMR as it seems some posts mentioned WRMR is experiential and not good for results reporting. Also, I'm not sure if appropriate to ask here, but when I try using LISREL with ML estimation (with u1 marked as categorical), it can still give model fit indices of Chi2, RMSEA, CFI, NNFI, SRMR, etc. Do you have any idea on the difference between Mplus and LISREL regarding the ML estimation in path analysis? Thank you very much. 


With ML for categorical outcomes there are no generally accepted overall tests of model fit available because the model is not a covariance structure model as with continuous outcomes. Instead of fitting a covariance matrix, you work with raw data. but you can check TECH10 for testing of pairs of variables and you can also test neighboring, nested models. And you can specify a saturated model and then use Model Test to check if some coefficients are zero. The difference between LISREL and Mplus in this regard is explained in Web Note 4, where I argue against the LISREL approach. 


Hello, I am running a crosslag model with both a continuous and dichotomous observed variables, using the WLSMV estimator. I am having some trouble deciding what coefficients to use and how to interpret the findings. For example: R1 and R2 = dichotomous E1 and E2 = continuous So, my syntax would be something like: R2 on R1 E1; E2 on R1 E1; I am assuming I can interpret the continuous regression as I would any standardized regression coefficient, but I am unclear how to interpret the regression with the dichotomous DV (R2 ON R1 E1). With a dichotomous DV I would typically use an odds ratio, so I do not really understand how to interpret the stdyx coefficients or what would be appropriate to report. Would it be possible to get an odds ratio instead? Any assistance would be greatly appreciated! 


WLSMV uses probit so odds ratios are essentially out of the picture. ML uses logit so you can work with odds ratios. But you may get slower computations due to many dimensions of integration  try it. With WLSMV you can use the standardized results and for binary outcomes they refer to a continuous latent response variable behind the binary observed. 

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